Question: Luis is 4 times as old as Brandon. Six years ago, Luis was 6 times as old as Brandon. How old is Brandon now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and Brandon. Let Luis's current age be $l$ and Brandon's current age be $b$ The information in the first sentence can be expressed in the following equation: $l = 4b$ Six years ago, Luis was $l - 6$ years old, and Brandon was $b - 6$ years old. The information in the second sentence can be expressed in the following equation: $l - 6 = 6(b - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = 4b$ . Substituting this into our second equation, we get: $4b$ $-$ $6 = 6(b - 6)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $4 b - 6 = 6 b - 36$ Solving for $b$ , we get: $2 b = 30.$ $b = 15$.